Novel forms of interpolator/decimator filter structure have been described recently in the literature. In particular, reference is made to the two articles: "Digital Signal Processing Schemes for efficient Interpolation and Decimation" by R. A. Valanzuala and A. G. Constantinides, reported in IEE. Proc. Vol. 130 No. 6 pp. 225-234 (December 1983); and, "Efficient Sampling Rate alteration using Recursive (IIR) Digital Filters" by R. Ansari and B. Lui, reported in IEEE Trans Acoust., Speech Sig Proc. Vol. ASSP-31 No. 6 pp. 1366-1373 (December 1983).
The structures described are capable of interpolating or decimating between two sampling rates related by a factor N where N is an integer. It proves most advantageous when N is 2, and it is this case that is considered further. It should be noted that Interpolation and Decimation between sampling rates differing by a factor of a power of two is easily implemented by a cascade of similar filters, each changing the frequency by a factor of two.
Important properties of these interpolator and decimator filter structures are as follows:
(i) The repeated use of simple All Pass Networks (APNs) to build up the filter structure, facilitating implementation,
(ii) Most of the signal processing is performed at the lower of the two sampling frequencies, reducing the number of multiplications and additions required per unit time to achieve a given performance requirement compared to alternative filter structures,
(iii) Good noise performance,
(iv) Low sensitivity of filter performance to coefficient value, resulting in short wordlength co-efficients,
(v) Reduced number of co-efficients required to implement a filter with given performance compared to alternative conventional filter structures.
However, there are some limitations to the performance of the filter structures as currently described in the literature. One of these limitations is that the frequency at which the attenuation of out of band signals increases to 3 dB is fixed at half of the lowest sampling frequency. This means that a filter to decimate from a 16 kHz to an 8 kHz sampling rate can only provide 3 dB attenuation of signals at 4 kHz. There are many applications which require the 3 dB point of the filter to be at some other frequency, so this is a severe limitation.